The boundary of a park is shaped like a circle. The park has a rectangular playground in the center and 2 square flower beds, one on each side of the playground. The length of the playground is l and its width is w. The length of each side of the flower beds is a. Which two equivalent expressions represent the total fencing material required to surround the playground and flower beds? Assume that the playground and beds do not overlap.
The total fencing material required to fence the playground and both flower beds is {2(1+w)+2(4a)} {2(1+w)+4a} {2(1w)+2a} {1w+4a} or {21+2w+8a} {21+2w+4a} {21w+2a} {1w+4a}
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Answers
Answer:
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The total fencing material required to fence the playground and both flower beds is {2(l+w)+2(4a)}.
Given:
The length of the rectangular playground= l
The width of the rectangular playground= w
The side of the flower bed= a
To find:
The total fencing material required to fence the playground and both flower beds.
Solution:
We can find the solution by following the steps given below-
We know that the fencing material will cover the perimeter of the rectangular playground and 2 flower beds.
So, we need to calculate the perimeter of the playground and square flower beds.
The perimeter of the rectangular playground= 2×(length+ width)
=2×(l+w)
=2(l+w)
The perimeter of the square flower bed=4× side
=4a
Since there are two flower beds, the total perimeter of flower beds= 2×4a
The total fencing material required= perimeter of the rectangular playground+ perimeter of two flower beds
= 2(l+w)+ 2×4a
={2(l+w)+2(4a)}
Therefore, the total fencing material required to fence the playground and both flower beds is {2(l+w)+2(4a)}.